Don’t worry if you score less than 50%, because it means you will learn something new when you check the solutions.

1. Maths jokes

It sounds odd, but there are maths jokes. Lots of jokes. In fact, lots of
mathematicians are very funny. Some of my favourite comedians (Dara O'Briain,
Romesh Ranganathan and Dave Gorman) studied maths at university, and I have
written a whole book about the mathematicians who write The Simpsons.

So, how good is your mathematical sense of humour? And how much maths do you
know? Below are 4 jokes with 3 possible punchlines each. Can you spot the correct punchline? You
will need to know a bit of maths in order to work out the right answer.

0.5 marks

1.1 Why is 6 afraid of 7?

Because 1, 2, 3

Because 7, 8, 9

Because 5 predates 6

The correct answer is (b), because it sounds like ”7 ate 9”.

0.5 marks

1.2 What are the 10 kinds of people in the world?

Set 0, Set 1, Set 2, …, Set 9

α, β, γ, δ, ε, ζ, η, θ, ι, κ

Those who understand binary, and those who don’t

In binary 10 = 2, so 10 kinds of people could mean 2 kinds of people. (If you haven’t covered binary maths yet then you have something to look forward to.)

0.5 marks

1.3 What does the “B” in Benoit B Mandelbrot stand for?

Benoit B Mandelbrot

Binomial

Breviation

This was a tough one. Benoit B Mandelbrot helped develop the mathematics of
fractals, which are structures or shapes that appear similar when you zoom in or
zoom out. Trees, clouds and certain mathematical shapes are fractals, as shown above. The bit of the tree in the red box looks just like the whole tree…
and you can zoom in even further and see more and more micro-replicas of the whole
tree.

The following video shows what happens if you zoom into the so-called Mandelbrot Set. You see the same pattern (a sort of seahorse’s tail) reappearing again, and again, and again:

So, returning to the joke, the B represents Benoit B Mandelbrot, because zooming into the name
gives you the whole name again.

0.5 marks

1.4 Why did the chicken cross the Möbius strip?

To get to the other… er…?

To reach a finite conclusion

To integrate itself into the tarmac

Another toughie – a Möbius strip is a strange mathematical shape which only has
one side, so you can’t get to the other side. As shown here, it is just a loop
with a single twist, but if you imagine running your finger along one side of
the loop you will find that your finger covers every bit of the loop... so it
only has one side. Möbius strips are fantastic, one of my favourite bits of
geometry, and we’ll return to them in next year’s Parallelogram series.

2. Mini cross-number

2 marks

2 A cross-number is like a crossword, but with numbers instead of letters. Solve the clues to find the digit x in this cross-number.

Across1. A cube3. A cube

Down1. One less than a cube2. A number

x = Correct Solution: 4

Show Hint (–1 mark)

–1 mark

1 across, 3 across & 1 down are all cubes (or one less than a cube) and they are all 2-digit numbers, which means they are between 10 and 99. There are not very many cube numbers between 10 and 99, so start by writing them down and then see how they might fit into the grid.

The correct answer is x = 4.

1 across, 3 across & 1 down are all cubes (or one less than a cube) and they are
all 2-digit numbers, which means they are between 10 and 99. The only cube
numbers between 10 and 99 are 27 and 64. So 1 across and 3 across must be 27 and
64, or 64 and 27. Meanwhile, 1 down must be 26 or 63. The cross-number only
works if 1 down is 26, because 3 across can then be 64, which means x = 4.

3. Maryam’s inspiration

You might be surprised to know that there is no Nobel Prize for maths. However,
there is an even bigger prize for mathematicians, which is called the Fields
Medal. It is only given every 4 years, so it is very rare and precious.

In 2014, Maryam Mirzakhani became the first woman to win a Fields Medal, but tragically she died just three years later. The Iranian-born NASA scientist, Firouz Naderi, wrote: “A light was turned off today, it breaks my heart... gone far too soon.”

Commenting on a piece of research she did alongside mathematician Alex Eskin, Mirzakhani said: “If we knew things would be so complicated, I think we would have given up... I don’t know, actually. I don’t know. I don’t give up easily.”

Mirzakhani was born in Iran and then worked in America, and you can find out about her life and work in the short video below.

Not surprisingly, Maryam talks about some incredibly complex maths, so don’t
worry if you find it confusing. In fact, if you think you understand what Maryam
is describing, then you probably don’t. Watch it carefully and answer the
question below.

1 mark

3.1 What indoor sport does Maryam mention in one of her mathematical
examples?

Chess

Darts

Billiards

Table tennis

Maryam talks about a problem involving the path of a ball bouncing around a
billiard table.

Maryam has said that she first became fired up about mathematics when her big
brother told her a story about the great mathematician Carl Friedrich Gauss.
When Gauss was a schoolboy, his teacher tried to keep the class busy by asking
them to add up all the numbers from 1 to 100.

However, before the teacher had even left the room, Gauss’s hand shot up and he
announced that the answer was 5,050.

Gauss was right, but how did he add up the first 100 numbers in just a few
seconds?

n+1 represents step 1, because you pair up all the numbers, so that all
the pairs add up to n+1.

n2 represents step 2, because the number of pairs is equal to the total
number of numbers divided by 2.

× represents step 3, because you then multiply the sum of each pair by
the number of pairs.

Let’s see if you can apply Gauss’s trick.

1 mark

3.2 Add up all the numbers from 1 to 50

Correct Solution: 1275

The correct answer is 1275.

1 mark

3.3 Add up all the numbers from 1 to 1,000

Correct Solution: 500500

The correct answer is 500500.

If you got either of these questions wrong, then take a look at
this website,
which goes into more detail about ways of adding the numbers from 1 to 100, and
is worth looking at.

4. Domino toppling

I watched this terrific video last week. Take a look and answer the question
afterwards.

1 mark

4 Starting with 5mm tall domino, roughly how many dominoes would you need to knock
down the Empire State Building?

30

100

30,000

100,000,000

Each domino can knock over a domino that is 1.5 times bigger, which does not seem
big, but when this happens over and over again, the dominoes get bigger and
bigger very quickly. This is known as exponential growth and we will return to
this in a future Parallelogram.

In the meantime, here is an even more extraordinary example of domino toppling
where the dominos get bigger and bigger. In fact, it was a world record at the
time.

5. Junior Maths Challenge Problem (UKMT)

1 mark

5 Consider the following three statements:

(i) Doubling a positive number always makes it larger.
(ii) Squaring a positive number always makes it larger.
(iii) Taking the positive square root of a positive number always makes it smaller.

Which statements are true?

All three

None

Only (i)

(i) and (ii)

(ii) and (iii)

The correct answer is just (i).

Statement (i) is true since 2x>x, if x>0.

Statement (ii) is not true. For example, (½)2 = ¼, which is not
larger than ½. Also, 12 is not bigger than 1.

Statement (iii) is also not true. For example, √¼ = ½, which is not smaller
than ¼. Also, √1 is not bigger than 1.

6. Weird optical illusions

The amazing, mind-warping objects in this video have been created by
mathematical artist and engineer Professor Kokichi Sugihara. These incredible
illusions literally mess with your brain.

Sometimes the geometry that you study at school might seem ordinary – what could be more ordinary than the angles of a triangle or the symmetry of a square? – but your teachers are really providing you with the first stepping stones towards gaining an understanding of the nature of space, and how you can build the sort of flabbergasting structures in this video.